Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 9 - Roots and Radicals - 9.4 - Products and Quotients Involving Radicals - Problem Set 9.4 - Page 418: 61



Work Step by Step

Multiplying by the conjugate of the denominator and using $(a+b)(a-b)=a^2-b^2,$ the given expression, $ \dfrac{10}{2-3\sqrt{3}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{10}{2-3\sqrt{3}}\cdot\dfrac{2+3\sqrt{3}}{2+3\sqrt{3}} \\\\= \dfrac{20+30\sqrt{3}}{(2)^2-(3\sqrt{3})^2} \\\\= \dfrac{20+30\sqrt{3}}{4-9\cdot3} \\\\= \dfrac{20+30\sqrt{3}}{4-27} \\\\= \dfrac{20+30\sqrt{3}}{-23} \\\\= -\dfrac{20+30\sqrt{3}}{23} .\end{array}
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